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arXiv · 2507.13726

On K3 surfaces with hyperbolic automorphism groups

Koji Fujiwara·Keiji Oguiso·Xun Yu
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Abstract

We show the finiteness of the N\'eron-Severi lattices of complex projective K3 surfaces whose automorphism groups are non-elementary hyperbolic with explicit descriptions, under the assumption that the Picard number $\ge 6$ which is optimal to ensure the finiteness. Our proof of finiteness is based on the study of genus one fibrations on K3 surfaces and recent work of Kikuta and Takatsu.

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Koji Fujiwara, Keiji Oguiso, Xun Yu. 2025-07-18. On K3 surfaces with hyperbolic automorphism groups. https://doi.org/10.1515/crelle-2026-0036

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